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Conservation of Angular Momentum of Particle

  1. The rate of change of angular momentum of a particle is equal to the torque produced by the total force. In a certain situation, the torque itself vanishes, then it follows that the angular momentum of the particle will remain constant. This is the law of conservation of the angular momentum of a particle.
  2. When the force becomes zero, the torque vanishes too. The particle then moves freely in a straight line in accordance with Newton's first law in which case both linear and angular momentum are conserved.
  3. A general situation is when the torque becomes zero without the force itself vanishing.
    The torque τ will vanish if the component F (the angular component) of F vanishes but the radial component F|| does not.
    The radial component F|| is the component of F along the radius (or position) vector r.
    Hence, if the force acting on the particle is purely radial (i.e. if it directed along or against its position vector) then the torque acting on the particle vanishes and its angular momentum is covered and so is its areal velocity.

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